A doubly accelerated degradation model based on the inverse Gaussian process and its objective Bayesian analysis

ABSTRACT

The accelerated degradation test (ADT) is an effective method for evaluating the lifetime of high-reliability products. In this paper, a doubly accelerated degradation model based on the inverse Gaussian process is proposed to characterize the ADT data, and then an objective Bayesian approach is presented to analyze the model. Some important noninformative priors including the Jeffreys prior and reference priors under different group orderings are derived. The propriety of the posterior distributions under each prior is validated. A simulation study is carried out to show the superiority of objective Bayesian approach compared with the parametric Bootstrap method. Finally, the approach is applied to analyze a carbon film data.

Keywords:

• Doubly accelerated degradation data
• inverse Gaussian process
• objective Bayesian
• Bootstrap

2010 Mathematics Subject Classification:

• 62F15

Acknowledgments

The authors are very grateful to the Editor-in-Chief, the Associate Editor and the two anonymous Reviewers for the careful review and valuable comments on earlier versions of this paper. He's work is supported by the National Natural Science Foundation of China (Grant No. 11201005), the Humanities and Social Sciences Foundation of Ministry of Education (Grant No. 17YJC910003), Anhui Provincal Natural Science Foundation (Grant No. 2008085MA08) and the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University), Ministry of Education (Grant No. KLATASDS1804). Cao's work is supported by the National Natural Science Foundation of China (Grant Nos. 11526070 and 11601008).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

He's work is supported by the National Natural Science Foundation of China (Grant No. 11201005), the Humanities and Social Sciences Foundation of Ministry of Education (Grant No. 17YJC910003), Anhui Provincial Natural Science Foundation (Grant No. 2008085MA08) and the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science (East China Normal University), Ministry of Education (Grant No. KLATASDS1804). Cao's work is supported by the National Natural Science Foundation of China (Grant Nos. 11526070 and 11601008).